Problem 3 (5 pr.) Consider the following linear program: Z = X₁ + 2x₂ + x3 X3 ≤ 2, x1 - x₂ + x3 = 1, 2x₁ - x₂ + x3 ≥ 2 x₁ ≥ 0, X₂ ≤0, x3 unrestricted. max s.t. X₁ + X₂ Use the weak duality theorem to show that z* ≤ 1 (Hint: find a proper feasible solution to the dual problem).

Fig: 1